Effective Elasticity Tensor of Fiber-Reinforced Orthorhombic Composite Materials with Fiber Distribution Parallel to Plane

An orthogonal composite material Ω with fibers consists of a matrix and orthothombic distribution fibers. In addition to the matrix properties, the fiber properties and the fiber volume fraction, the effective (macroscopic) elastic stress–strain constitutive relation of Ω is related to the fiber direction distribution. Until now, there have been few papers that give an explicit formula of the macroscopic elastic stress–strain constitutive relation of Ω with the effect of the fiber direction distribution. Taking the expanded coefficients of the Fourier series as the fiber direction distribution coefficients, we give a formula of the fiber direction distribution parallel to a plane computed through the fiber directions. By the self-consistent estimates, we derive an explicit formula of the macroscopic elastic stress–strain constitutive relation of Ω with the fiber direction distribution coefficients. Since all tensors are represented in Kelvin notation, the macroscopic elastic stress–strain constitutive relation of Ω can be derived and computed only by matrix manipulations. To check the explicit formula, we use the FEM computation to obtain the macroscopic elastic stress–strain relation of Ω for three examples. The computational results of the explicit formula for the three examples are consistent with those of the FEM simulations

Constitutive Relations of Anisotropic Polycrystals: Self-Consistent Estimates

In this paper, the elastic constitutive relation of polycrystals contains the effect of the mesostucture coefficients. We consider a general case and derive the average elastic constitutive relation pertaining to polycrystals of cubic crystals with any symmetry of crystalline orientation in their statistical distribution. Following Budiansky and Wu, we used self-consistent estimates of eigenstrain to obtain the effective elastic constitutive relation of polycrystals in an explicit form. For the Voigt assumption and the Reuss assumption, the effective elastic constitutive relation of polycrystals on cubic crystals contains the the mesostructure coefficients up to linear terms. In general, the linear term expression works well for materials such as aluminum, the single crystal of which has weak anisotropy. However the same expression (which allows the anisotropic part of the effective elastic constitutive relation to depend only linearly on the mesostructure coefficients) does not suffice for materials such as copper, in which the single crystal is strongly anisotropic. Per the Taylor theorem, we expand the expression based on the self-consistent estimates with respect to the mesostructure coefficients up to quadratic terms for anisotropic polycrystals of cubic crystals. While our numerical data are very close to those of Morris, our expression is much simpler

Effect of yttrium content on microstructure and tensile properties of as-cast and as-solutionized Al-Zn-Mg-Cu alloys

Four kinds of 7xxx series aluminum alloys with different Y elementcontents were obtained by ordinary gravity casting. The effect of Y content on the microstructure and mechanical properties of as-cast and as-solutionized Al-7.9Zn-3Mg-2.4Cu-0.13Zr (wt%) alloys were investigated by means of x-ray diffraction (XRD), electron backscattering diffraction (EBSD), scanning electron microscopy (SEM), energy dispersive spectrometer (EDS) and room-temperature tensile tests. The results shows that, in as-cast condition, Y element can refine the grain and reduce the content of Mg(Zn, Cu, Al) _2 lamellar phases at the interdendritic. (Al, Zn) _8 Cu _4 Y block-shaped phases form in interdendritic regions. After solution treatment, the undissolved Mg(Zn, Cu, Al) _2 phases evolved from lamellar to bulk-like which distribution in interdendritic, but no obvious change in (Al, Zn) _8 Cu _4 Y phase. The tensile testing results shows that the optimal yttrium content is 0.45 wt%. At 0.45 wt% Y, the ultimate tensile strength and elongation are 267 MPa and 2.4% in as-cast condition and 420 MPa and 3.6% in as-solutionized condition

Machine-learning assisted compositional optimization of 2xxx series aluminum alloys towards tensile strength

High-strength 2xxx series aluminum alloys (Al-Cu system) have been favored by the aerospace and railway transportation industries. Traditionally, developing new materials with targeted properties is guided by extensive experiments and expert experience, causing the development process to be dismayingly slow and expensive. Here, a Kriging model-based efficient global optimization(EGO) lgorithm is applied to search for new 2xxx series aluminum alloys with high tensile strength in a huge search space. After four iterations, the alloy’s ultimate tensile strength increased by 60 MPa, which is higher than that of the best alloy in the initial data set. This study demonstrates the feasibility of using machine-learning to search for 2xxx alloys with good mechanical performance